$SO\left(32\right)$ heterotic line bundle models

We search for the three-generation standard-like and/or Pati-Salam models from the $SO\left(32\right)$ heterotic string theory on smooth, quotient complete intersection Calabi-Yau threefolds with multiple line bundles, each with structure group $U\left(1\right)$. These models are S- and T-dual to intersecting D-brane models in type IIA string theory. We find that the stable line bundles and Wilson lines lead to the standard model gauge group with an extra $U(1{)}_{B-L}$ via a Pati-Salam-like symmetry and the obtained spectrum consists of three chiral generations of quarks and leptons, and vector-like particles. Green-Schwarz anomalous $U\left(1\right)$ symmetries control not only the Yukawa couplings of the quarks and leptons but also the higher-dimensional operators causing the proton decay.